Optimize the following Boolean expressions using a map• F(W,X,Y,Z)=Em(0,1,2,4,7,8,10,12)Obtain Truth table of the following function and express each function in Sum of Minterms andProduct of Maxterms form:• WXY'+WXZ'+WXZ+YZ'

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Optimize the following Boolean expressions using a map
• F(W,X,Y,Z)=Em(0,1,2,4,7,8,10,12)
Obtain Truth table of the following function and express each function in Sum of Minterms and
Product of Maxterms form:
• WXY'+WXZ'+WXZ+YZ'

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Step 1

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Given

F(W, X, Y, Z) = Σm(0, 1, 2, 4, 7, 8, 10, 12)

Procedure for optimizing the given oolean expression using k-map:

Select K-map according to the number of variables.
Identify minterms or max terms as given in the problem.
For SOP put 1’s in blocks of K-map respective to the minterms (0’s elsewhere).
Make rectangular groups containing total terms in the power of two like 2,4,8 ..(except 1) and try to cover as many elements as you can in one group.
From the groups made in step 4 find the product terms and sum them up for SOP form.

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